Regarding Tomas-- the Braves were serious about him, but Hart refused to entertain the idea of an opt-out. No formal offer was made but parameters were discussed and the Braves were not shying away from his salary expectations (or what he ultimately got from LaRussa and family). The opt-out ended talks pretty abruptly.
Regarding Lester-- they were doing their diligence on him as a Georgia resident, free agent, pitcher, would be a good fit in the clubhouse, etc. They met- did not discuss numbers- and no offer was made. The Braves, after hearing some of the numbers being thrown about for Lester, decided that he's too rich for their blood and that was the end of it. It wasn't meant to be a PR plug for the Braves- it was just an introductory meeting.
One thing is for sure about the Hart-JC led FO; they do not like to waste people's time (their own included). So if a player's own valuation is significantly different from the team's, they aren't just "going to make an offer" for the sake of making one. The Braves are very deliberate in their overtures when the time comes.
To be clear, I'm not saying I always agree with their moves. I did agree with the Heyward decision after learning what he was expecting (and now will likely test the FA waters and get that or more assuming he plays as expected in 2015 or better). I wouldn't be a huge fan of Markakis at the current numbers being thrown about; I'd rather go for Headley for the same cost, dump CJ somewhere and see what we can do in the OF (Aoki as a low cost option, or someone better via trade).
Most "inside information" anyone here's going to get, and likely as much as the celebrated scoopers (Rosenthal et al) will ever get either.
Thanks for the clarification ramadon.